Albert Einstein once famously described compound interest as the eighth wonder of the world -- and he knew a thing or two.
Though I vaguely remember being taught about it in school maths class, its power when it comes to savings and investments were really never made clear to me and it took me a while before I realised its true magic.
If you suggest an interest rate of 5% per year and ask most people what they think it's likely to return over the long term, many will expect a doubling in 20 years. They'll just go on simple interest and forget that each year you also get 5% of last year's 5%, and so on.
The difference that can make can be surprising. Instead of £100 doubling in 20 years based on simple interest, the effect of compounding would actually take it to £265. And it would only take a little over 14 years to double your money, not 20.
When you keep the money in for longer, the effects grow enormously. The same £100 invested for 40 years would grow to £300 based on simple interest alone, but with compounding you'd end up with more than £700. The interest on the interest will be worth twice as much as the interest on your original £100.
It really is the way to keep ahead of inflation.
Shares are best
Compounding works the same way when you invest in shares too, notably those paying high dividends. A lot of investors will take their dividend cash to live on, which is a sensible way to fund your retirement. But if you don't need the cash yet, using your dividends to buy more shares can result in a far bigger retirement nest egg.
Royal Dutch Shell is one of our top FTSE 100 dividend shares, and I've been tracking its share price and dividends since 2004 and calculating overall returns.
If you'd invested £10,000 in Shell shares back then, you'd have seen the value of your shares rise to £15,700 today. That's not a bad return over 14 years, especially considering it spans the dip during the oil price crash.
But that ignores dividends, and if you'd taken the cash every year you'd see your total up to £25,800. Now, what about the compounding effect of reinvesting your dividends in new Shell shares? If you'd done that, you'd be sitting on a cool £31,800 worth of shares -- with reinvesting adding £6,000 to your nest egg.
And there are two other big benefits. You'd have made the most of the share price dip during the oil crisis by buying even more shares when they were down. And you would now be sitting on a little over 1,300 Shell shares instead of the 700 or so you'd have bought with your original £10,000. Your next 14 years should be even more profitable than your first 14.
If that's not enough to convince you of the miracle of compounding returns, let me tell you of my favourite stock market statistic.
Barclays has been analysing stock market returns since 1899, and they calculate that £100 invested in UK shares in 1945 would have grown to a little over £9,000 even after accounting for inflation. A 90-fold gain is pretty nice.
But that's with dividends taken and spent every year. If you'd reinvested them instead, you'd have made a massive £179,000!
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Alan Oscroft has no position in any of the shares mentioned. The Motley Fool UK has recommended Barclays and Royal Dutch Shell. Views expressed on the companies mentioned in this article are those of the writer and therefore may differ from the official recommendations we make in our subscription services such as Share Advisor, Hidden Winners and Pro. Here at The Motley Fool we believe that considering a diverse range of insights makes us better investors.